Averaging of second-order periodic equations with elastic and rigid constraints

Averaging of second-order periodic equations with elastic and rigid constraints
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A mass-spring oscillator colliding with an obstacle is considered in this talk.

A mass-spring oscillator colliding with an obstacle is considered in this talk. It is known that for the simplest linear oscillator without excitation the phase portrait is formed by a family of closed curves of some constant period. Nonlinear periodic perturbations destroy this family creating isolated periodic solutions (resonances). Approximate amplitudes and stability of these solutions can be determined using the classical averaging method. In the talk I will describe how the averaging method is violated (and which new phenomena this method can predict) if the system under consideration contains elastic or rigid constraints. It will be shown, in particular, that unlike the classical smooth situation the Floquet multipliers of some resonance periodic solutions no longer converge to +1 (as the amplitude of the perturbation decreases) remaining far inside the unit circle.

Speaker
Dr Oleg Makarenkov (Imperial College London)
Venue
FN 111